Number Theory in the Spirit of Liouville
Kenneth S. Williams (Author)
The only book entirely devoted to Joseph Liouville's elementary method in number theory, this gentle introduction explains his method in a clear and straightforward manner, including many applications. This is an extremely valuable resource suitable for advanced undergraduate and beginning graduate students, and researchers in number theory.
1 online resource (306 pages)
9780511751684, 9781107002531, 9780521175623, 0511751680, 1107002532, 0521175623
1170588164
Preface; 1. Joseph Liouville (1809–1888); 2. Liouville's ideas in number theory; 3. The arithmetic functions σk(n), σk*(n), dk,m(n) and Fk(n); 4. The equation i2 + jk = n; 5. An identity of Liouville; 6. A recurrence relation for σ*(n); 7. The Girard–Fermat theorem; 8. A second identity of Liouville; 9. Sums of two, four and six squares; 10. A third identity of Liouville; 11. Jacobi's four squares formula; 12. Besge's formula; 13. An identity of Huard, Ou, Spearman and Williams; 14. Four elementary arithmetic formulae; 15. Some twisted convolution sums; 16. Sums of two, four, six and eight triangular numbers; 17. Sums of integers of the form x2+xy+y2; 18. Representations by x2+y2+z2+2t2, x2+y2+2z2+2t2 and x2+2y2+2z2+2t2; 19. Sums of eight and twelve squares; 20. Concluding remarks; References; Index.